As per the other replies iTunes even the latest version does not itself support FLAC.
On a Mac it is probably possible to get iTunes to play FLAC files but as you will see, not in iTunes for Windows (which you appear to be using).
For the benefit of everyone here is how to do FLAC in iTunes for Mac.
1. First you need a FLAC codec for QuickTime which is available for both Mac and Windows here
http://www.xiph.org/quicktime/download.html
However apparently this only supports FLAC in an Ogg container and not in the more normal FLAC file format. On a Mac someone else has written a FLAC importer for QuickTime
2. FLAC importer for QuickTime detailed here
http://barelyfocused.net/blog/2006/10/12/native-flac-in-itunesquicktime/
It maybe that you could port the above to Windows.
However in my opinion, you should switch to using Apple Lossless instead. Remember as FLAC and Apple Lossless are both lossless formats you can convert between them without losing any quality.
Originally, it was thought that FLAC being open source (and lossless of course) was the best option for a lossless format without being locked in to a restrictive format (e.g. WMA lossless, or as originally thought Apple Lossless). However as you can see FLAC locks you out of iTunes (effectively) and iPod (and iPhone, and Apple TV).
Apple Lossless was originally thought to be limited to only Apple products (iTunes, iPod, etc.) but some time ago it was reverse engineered so that it could be used in Mplayer, VLC, Foobar 2000, etc. This represented significant progress but still did not support Windows Media Player or Media Center. However I came up with a solution that combined the BASS audio library, an existing Apple Lossless module for BASS, and a conversion of BASS plus an MP3 module in to a directshow filter (that worked in WMP). I got the programmer (Milenko Mitrovic) of that BASS+MP3 directshow filter to do a BASS+Apple Lossless conversion to a directshow filter using the same approach (the Apple Lossless module is open source) and now it is possible to add Apple Lossless files to Windows Media Player and play them just fine and hence also in Media Center.
See the January 8th 2007 entry on Milenko's website here
http://www.dsp-worx.de/
As a result it is now possible to use Apple Lossless with all of the below (and probably others as well)
iTunes (of course)
iPod (of course)
TV (of course)
iPhone
Windows Media Player (yes really!)
Media Center (yes really!)
Xbox 360 Media Extender (yes really!)
Roku Soundbridge
SlimDevices Squeezebox
Sonos ZonePlayer
Foobar 2000
WinAmp
dbPowerAmp
VLC
MPlayer